论文标题
在紧凑的Riemann表面上的捆绑价值伯格曼空间的尺寸
On the dimension of bundle-valued Bergman spaces on compact Riemann surfaces
论文作者
论文摘要
考虑到紧凑型Riemann Surface $ m $上的Holomorthic Vector Bundle $ e $，以及$ M $中的开放式$ D $ $ D $，我们证明，将$ e $ to $ e $ to $ e $ to $ e $ to $ e $ to $ e $ to $ e $ d $的伯格曼空间与全球全球荷兰式$ $ $ $ $ $ $ $ e $ $ e $ cosional of Infrinite cosionals of Infrosional或be be be be be be be beementions cosigine cosine of Bergman Space。此外，我们完全根据$ d $的潜在理论特性来表征后者。
Given a holomorphic vector bundle $E$ over a compact Riemann surface $M$, and an open set $D$ in $M$, we prove that the Bergman space of holomorphic sections of the restriction of $E$ to $D$ must either coincide with the space of global holomorphic sections of $E$, or be infinite dimensional. Moreover, we characterize the latter entirely in terms of potential-theoretic properties of $D$.
